{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "import numpy as np\n",
    "import sympy as sy\n",
    "sy.init_printing() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def round_expr(expr, num_digits):\n",
    "    return expr.xreplace({n : round(n, num_digits) for n in expr.atoms(sy.Number)})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Systems of First-Order Equations</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In time series analysis, we study difference equations by writing them into a linear system. For instance,\n",
    "\n",
    "$$\n",
    "3y_{t+3} - 2y_{t+2} + 4y_{t+1} - y_t = 0\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define \n",
    "\n",
    "$$\n",
    "\\mathbf{x}_t = \n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "y_t\\\\\n",
    "y_{t+1}\\\\\n",
    "y_{t+2}\n",
    "\\end{matrix}\n",
    "\\right], \\qquad\n",
    "\\mathbf{x}_{t+1} = \n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "y_{t+1}\\\\\n",
    "y_{t+2}\\\\\n",
    "y_{t+3}\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Rerrange the difference equation for better visual shape,\n",
    "\n",
    "$$\n",
    "y_{t+3} = \\frac{2}{3}y_{t+2} - \\frac{4}{3}y_{t+1} + \\frac{1}{3}y_{t}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The difference equation can be rewritten as\n",
    "\n",
    "$$\n",
    "\\mathbf{x}_{t+1} = A \\mathbf{x}_{t}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That is,\n",
    "\n",
    "$$\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "y_{t+1}\\\\\n",
    "y_{t+2}\\\\\n",
    "y_{t+3}\n",
    "\\end{matrix}\n",
    "\\right] = \n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "0 & 1 & 0\\\\\n",
    "0 & 0 & 1\\\\\n",
    "\\frac{1}{3} & -\\frac{4}{3} & \\frac{2}{3}\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "y_t\\\\\n",
    "y_{t+1}\\\\\n",
    "y_{t+2}\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In general, we make sure the difference equation look like:\n",
    "\n",
    "$$\n",
    "y_{t+k} = a_1y_{t+k-1} + a_2y_{t+k-2} + ... + a_ky_{t}\n",
    "$$\n",
    "\n",
    "then rewrite as $\\mathbf{x}_{t+1} = A \\mathbf{x}_{t}$, where\n",
    "\n",
    "$$\n",
    "\\mathbf{x}_t = \n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "y_{t}\\\\\n",
    "y_{t+1}\\\\\n",
    "\\vdots\\\\\n",
    "y_{t+k-1}\n",
    "\\end{matrix}\n",
    "\\right], \\quad\n",
    "\\mathbf{x}_{t+1} = \n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "y_{t+1}\\\\\n",
    "y_{t+2}\\\\\n",
    "\\vdots\\\\\n",
    "y_{t+k}\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And also\n",
    "\n",
    "$$A=\\left[\\begin{array}{ccccc}\n",
    "0 & 1 & 0 & \\cdots & 0 \\\\\n",
    "0 & 0 & 1 & & 0 \\\\\n",
    "\\vdots & & & \\ddots & \\vdots \\\\\n",
    "0 & 0 & 0 & & 1 \\\\\n",
    "a_{k} & a_{k-1} & a_{k-2} & \\cdots & a_{1}\n",
    "\\end{array}\\right]$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Markov Chains</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Markov chain is a type of stochastic process, commonly modeled by difference equation, we will be slightly touching the surface of this topic by walking through an example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Markov chain is also described by the first-order difference equation $\\mathbf{x}_{t+1} = P\\mathbf{x}_t$, where $\\mathbf{x}_t$ is called <font face=\"gotham\" color=\"red\">state vector</font>, $A$ is called <font face=\"gotham\" color=\"red\">stochastic matrix</font>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose there are 3 cities $A$, $B$ and $C$, the proportion of population migration among cities are constructed in the stochastic matrix below"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "M = \n",
    "\\left[\n",
    "\\begin{matrix}\n",
    ".89 & .07 & .10\\\\\n",
    ".07 & .90 & .11\\\\\n",
    ".04 & .03 & .79\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For instance, the first column means that $89\\%$ of population will stay in city $A$, $7\\%$ will move to city $B$ and $4\\%$ will migrate to city $C$. The first row means $7\\%$ of city $B$'s population will immigrate into $A$, $10\\%$ of city $C$'s population will immigrate into $A$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose the initial population of 3 cities are $(593000, 230000, 709000)$, convert the entries into percentage of total population."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.38707572, 0.15013055, 0.46279373])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([593000, 230000, 709000])\n",
    "x = x/np.sum(x);x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Input the stochastic matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "M = np.array([[.89, .07, .1], [.07, .9, .11], [.04, .03, .79]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After the first period, the population proportion among cities are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.4012859 , 0.2131201 , 0.38559399])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1 = M@x\n",
    "x1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second period"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.41062226, 0.26231345, 0.3270643 ])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2 = M@x1\n",
    "x2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The third period"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.41652218, 0.30080273, 0.28267509])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x3 = M@x2\n",
    "x3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can construct a loop till $\\mathbf{x}_{100} = M\\mathbf{x}_{99}$, then plot the dynamic path. Notice that the curve is flattening after 20 periods, and we call it <font face=\"gotham\" color=\"red\">convergence to steady-state</font>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 100\n",
    "X = np.zeros((k, 3))\n",
    "X[0] = M@x\n",
    "i = 0\n",
    "\n",
    "while i+1 < 100:\n",
    "    X[i+1] = M@X[i]\n",
    "    i = i + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (12, 12))\n",
    "\n",
    "la = ['City A', 'City B', 'City C']\n",
    "s = '$%.3f$'\n",
    "for i in [0, 1, 2]:\n",
    "    ax.plot(X[:, i], lw = 3, label = la[i] )\n",
    "    ax.text(x = 20, y = X[-1,i], s = s %X[-1,i], size = 16)\n",
    "\n",
    "ax.axis([0, 20, 0, .6]) # No need to show more of x, it reaches steady-state around 20 periods\n",
    "ax.legend(fontsize = 16)\n",
    "ax.grid()\n",
    "ax.set_title('Dynamics of Population Percentage')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Eigenvalue and -vector in Markov Chain</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the $M$ in last example is diagonalizable, there will be $n$ linearly independent eigenvectors and corresponding eigenvalues, $\\lambda_1$,...,$\\lambda_n$. And eigenvalues can always be arranged so that $\\left|\\lambda_{1}\\right| \\geq\\left|\\lambda_{2}\\right| \\geq \\cdots \\geq\\left|\\lambda_{n}\\right|$. \n",
    "\n",
    "Also, because any initial vector $\\mathbb{x}_0 \\in \\mathbb{R}^n$, we can use the basis of eigenspace (eigenvectors) to represent all $\\mathbf{x}$.\n",
    "\n",
    "$$\n",
    "\\mathbf{x}_{0}=c_{1} \\mathbf{v}_{1}+\\cdots+c_{n} \\mathbf{v}_{n}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is called <font face=\"gotham\" color=\"red\">eigenvector decomposition</font> of $\\mathbf{x}_0$. Multiply by $A$\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mathbf{x}_{1}=A \\mathbf{x}_{0} &=c_{1} A \\mathbf{v}_{1}+\\cdots+c_{n} A \\mathbf{v}_{n} \\\\\n",
    "&=c_{1} \\lambda_{1} \\mathbf{v}_{1}+\\cdots+c_{n} \\lambda_{n} \\mathbf{v}_{n}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "In general, we have a formula for $\\mathbf{x}_k$\n",
    "\n",
    "$$\n",
    "\\mathbf{x}_{k}=c_{1}\\left(\\lambda_{1}\\right)^{k} \\mathbf{v}_{1}+\\cdots+c_{n}\\left(\\lambda_{n}\\right)^{k} \\mathbf{v}_{n}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we test if $M$ has $n$ linearly independent eigvectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.89 & 0.07 & 0.1\\\\0.07 & 0.9 & 0.11\\\\0.04 & 0.03 & 0.79\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡0.89  0.07  0.1 ⎤\n",
       "⎢                ⎥\n",
       "⎢0.07  0.9   0.11⎥\n",
       "⎢                ⎥\n",
       "⎣0.04  0.03  0.79⎦"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = sy.Matrix([[.89, .07, .1], [.07, .9, .11], [.04, .03, .79]]);M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.is_diagonalizable()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$M$ is diagonalizable, which also means that $M$ has $n$ linearly independent eigvectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}177.0 & -0.4641 & 6.4641\\\\191.0 & -0.5359 & -7.4641\\\\61.0 & 1.0 & 1.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡177.0  -0.4641  6.4641 ⎤\n",
       "⎢                       ⎥\n",
       "⎢191.0  -0.5359  -7.4641⎥\n",
       "⎢                       ⎥\n",
       "⎣61.0     1.0      1.0  ⎦"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P, D = M.diagonalize()\n",
    "P = round_expr(P,4); P # user-defined round function at the top of the notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0 & 0.0 & 0.0\\\\0.0 & 0.7554 & 0.0\\\\0.0 & 0.0 & 0.8246\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1.0   0.0     0.0  ⎤\n",
       "⎢                   ⎥\n",
       "⎢0.0  0.7554   0.0  ⎥\n",
       "⎢                   ⎥\n",
       "⎣0.0   0.0    0.8246⎦"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D = round_expr(D,4); D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we find the $\\big[\\mathbf{x}_0\\big]_C$, i.e. $c_1, c_2, c_3$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.387\\\\0.1501\\\\0.4627\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡0.387 ⎤\n",
       "⎢      ⎥\n",
       "⎢0.1501⎥\n",
       "⎢      ⎥\n",
       "⎣0.4627⎦"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x0 = sy.Matrix([[.3870], [.1501], [0.4627]]);x0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0 & 0.0 & 0.0 & 0.0023\\\\0.0 & 1.0 & 0.0 & 0.3027\\\\0.0 & 0.0 & 1.0 & 0.0178\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1.0  0.0  0.0  0.0023⎤\n",
       "⎢                     ⎥\n",
       "⎢0.0  1.0  0.0  0.3027⎥\n",
       "⎢                     ⎥\n",
       "⎣0.0  0.0  1.0  0.0178⎦"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P_aug = P.row_join(x0)\n",
    "P_aug_rref = round_expr(P_aug.rref()[0],4); P_aug_rref"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.0023\\\\0.3027\\\\0.0178\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡0.0023⎤\n",
       "⎢      ⎥\n",
       "⎢0.3027⎥\n",
       "⎢      ⎥\n",
       "⎣0.0178⎦"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = sy.zeros(3, 1)\n",
    "for i in [0, 1, 2]:\n",
    "    c[i] = P_aug_rref[i, 3]\n",
    "c = round_expr(c,4);c "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can use the formula to compute $\\mathbf{x}_{100}$, it is the same as we have plotted in the graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.4071\\\\0.4393\\\\0.1403\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡0.4071⎤\n",
       "⎢      ⎥\n",
       "⎢0.4393⎥\n",
       "⎢      ⎥\n",
       "⎣0.1403⎦"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x100 = c[0] * D[0, 0]**100 * P[:, 0]\\\n",
    "+ c[1] * D[1, 1]**100 * P[:, 1]\\\n",
    "+ c[2] * D[2, 2]**100 * P[:, 2]\n",
    "x100 = round_expr(x100,4);x100 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is close enough to the steady-state."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Fractal Pictures</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is an example of fractal geometry, illustrating how dynamic system and affine transformation can create fractal pictures."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The algorithem is perform 4 types of affine transformation. The corresponding probabilites are $p_1, p_2, p_3, p_4$.\n",
    "\n",
    "$$\n",
    "\\begin{array}{l}\n",
    "T_{1}\\left(\\left[\\begin{array}{l}\n",
    "x \\\\\n",
    "y\n",
    "\\end{array}\\right]\\right)=\\left[\\begin{array}{rr}\n",
    "0.86 & 0.03 \\\\\n",
    "-0.03 & 0.86\n",
    "\\end{array}\\right]\\left[\\begin{array}{l}\n",
    "x \\\\\n",
    "y\n",
    "\\end{array}\\right]+\\left[\\begin{array}{l}\n",
    "0 \\\\\n",
    "1.5\n",
    "\\end{array}\\right], p_{1}=0.83 \\\\\n",
    "T_{2}\\left(\\left[\\begin{array}{l}\n",
    "x \\\\\n",
    "y\n",
    "\\end{array}\\right]\\right)=\\left[\\begin{array}{lr}\n",
    "0.2 & -0.25 \\\\\n",
    "0.21 & 0.23\n",
    "\\end{array}\\right]\\left[\\begin{array}{l}\n",
    "x \\\\\n",
    "y\n",
    "\\end{array}\\right]+\\left[\\begin{array}{l}\n",
    "0 \\\\\n",
    "1.5\n",
    "\\end{array}\\right], p_{2}=0.09 \\\\\n",
    "T_{3}\\left(\\left[\\begin{array}{l}\n",
    "x \\\\\n",
    "y\n",
    "\\end{array}\\right]\\right)=\\left[\\begin{array}{rr}\n",
    "-0.15 & 0.27 \\\\\n",
    "0.25 & 0.26\n",
    "\\end{array}\\right]\\left[\\begin{array}{l}\n",
    "x \\\\\n",
    "y\n",
    "\\end{array}\\right]+\\left[\\begin{array}{l}\n",
    "0 \\\\\n",
    "0.45\n",
    "\\end{array}\\right], p_{3}=0.07 \\\\\n",
    "T_{4}\\left(\\left[\\begin{array}{l}\n",
    "x \\\\\n",
    "y\n",
    "\\end{array}\\right]\\right)=\\left[\\begin{array}{ll}\n",
    "0 & 0 \\\\\n",
    "0 & 0.17\n",
    "\\end{array}\\right]\\left[\\begin{array}{l}\n",
    "x \\\\\n",
    "y\n",
    "\\end{array}\\right]+\\left[\\begin{array}{l}\n",
    "0 \\\\\n",
    "0\n",
    "\\end{array}\\right], p_{4}=0.01\n",
    "\\end{array}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The codes below are self-explanatory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = np.array([[[.86, .03],\n",
    "              [-.03, .86]],\n",
    "             [[.2, -.25],\n",
    "              [.21, .23]],\n",
    "             [[-.15, .27],\n",
    "              [.25, .26]],\n",
    "             [[0., 0.],\n",
    "              [0., .17]]])\n",
    "a = np.array([[[0,1.5]],\n",
    "             [[0,1.5]],\n",
    "             [[0,0.45]],\n",
    "             [[0,0]]])\n",
    "\n",
    "p1 = 1*np.ones(83)\n",
    "p2 = 2*np.ones(9)\n",
    "p3 = 3*np.ones(7)\n",
    "p4 = 4*np.ones(1)\n",
    "p = np.hstack((p1,p2,p3,p4))\n",
    "\n",
    "k = 30000\n",
    "fig, ax = plt.subplots(figsize = (5,8))\n",
    "X = np.zeros((2,k))\n",
    "for i in range(k-1):\n",
    "    n = np.random.randint(0, 100)\n",
    "    if p[n] == 1:\n",
    "        X[:,i+1] = A[0,:,:]@X[:,i]+a[0,:,:]\n",
    "    elif p[n] == 2:\n",
    "        X[:,i+1]  = A[1,:,:]@X[:,i]+a[1,:,:]\n",
    "    elif p[n] == 3:\n",
    "        X[:,i+1]  = A[2,:,:]@X[:,i]+a[2,:,:]\n",
    "    else:\n",
    "        X[:,i+1]  = A[3,:,:]@X[:,i]+a[3,:,:]\n",
    "ax.scatter(X[0,:],X[1,:], s = 1, color = 'g')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
